Consider the following linear programming problem

if A and B are the two binding constraints.

(Round to ONLY two digits after decimal points)

a) What is the range of optimality of the objective function?

  .......... ≤ C1/C2  ≤  ............

b) Suppose that the unit revenues for X1 and X2 are changed to $100 and $18, respectively. Will the current optimum remain the same?

............... that because the new C1/C2 is ........... which is .............. the range of optimality

c) Suppose that the unit revenue of X1 is fixed $4. What is the associated range for the unit revenue for X2 that will keep the optimum unchanged?

   .......... ≤ C2 ≤  ............

d) The Shadow Price for Constraint A is ..........

e) The Shadow Price for Constraint B is .........

f) If only the capacity of Constraint A is increased from the present 40 hours to 45 hours, The increase in revenue will be = $..........

g) A suggestion is made to increase the capacities of Constraint A and B by an hour at the additional cost of $1/hr. Is this advisable?

This is advisable for .............. and the total additional net revenue per hour would be $............

Complete the attached worksheet. You will need to show your work for each question

1) CircumSpect Products produces a home sentry system, easily installed by a homeowner, that they can produce and ship at a cost of $214 per unit. The company has fixed costs of $11,000 per month. The company believes it can position the product as an upscale specialty item and retail it for $995, or it can use a broader market strategy and sell it for $495. Calculate the required breakeven level of sales, to include $4,000 per month in profit, at each of these prices. Next, discuss their profit levels at each price, assuming they sell twice as many units as they need to in order to breakeven.

2) Serenity Senior Retirement Home has a capacity of 100 residents. It estimates that it has a variable cost of $450/month per resident (to include room, board, and personalized attention), and fixed costs of $5,700 per month. Assuming they operate at a 92% occupancy rate, what price per resident per month must they charge in order to earn a monthly profit of $8,000?

1. The demand function for the Baye Firm is: P = 100 – 0.5 Q

The firm’s total cost function is: 1500 – 10 Q + 0.5Q2

(a) Is this a perfectly competitive firm? (5 Points)

(b) Find the output level and price at which the firm’s total revenue is maximized. (10 Points)

(c) Find the output level and price at which the firm’s total profit is maximized. (10 Points)

(d) Is demand elastic, unitary elastic, or inelastic at the output level where total revenue
is maximized? (10 Points)

(e) Is demand elastic, unitary elastic, or inelastic at the output level where total profit
is maximized? (10 Points)

(f) What is the value of the firm’s total fixed cost at the output level where total revenue
is maximized? What about at the output level where total profit is maximized? (10 Points)

(g) What is the value of the firm’s average variable cost at the output level where total
revenue is maximized? What about at the output level where total profit is
maximized? (10 Points)

Selling price is $10/tin. The cost is $8/tin This includes $6 of direct material and $1.50 of direct labor. Direct labor is 1 hour per 100 tins. Annual manufacturing overhead is estimated at $100,000 for the expected sales of 200,000 tins. The breakdown for manufacturing overhead includes 85% of variable costs.

1a. What is the standard fixed manufacturing overhead cost per tin?

b. The Volume Variance is $750 Favorable. How many units were actually produced during the year?

c. How much is total budgeted fixed manufacturing overhead?

d. The Controllable Variance is $3250 Unfavorable. What was the total dollar amount for actual manufacturing overhead?

e. What are the total standard hours allowed for actual production?

6. The Labor Quantity Variance is $300 Unfavorable. How many total actual hours were worked?

7. What is the total standard cost of direct materials for total actual production?

8. Total Material Price Variance is $16,800 Unfavorable. What was the actual direct material cost for total actual production?

13. Which of the following statements is INCORRECT about trading on margin A. It is a leveraged equity investment. B. Stocks purchased on margin are registered in street name. C. It increases payoff both on the upside and downside. D. In general, a limit-buy order may be placed to limit potential losses.

17. Consider the following short sale example: an investor borrows 100 shares of a stock from the broker, put down 50% as the initial margin, and sells the stock at $50/share in the market. If the maintenance margin is 30%, how much can the stock price rise before the investor gets a margin call?

      A. 56.79

      B. 57.69

      C. 59.69

      D. 58.79

18. Regarding the previous question, suppose the stock price later goes up from $50/share to $75/share, put a ____________may limit the potential loss for the investor?

      A. limit sell order at $60/share

      B. limit buy order at $60/share

      C. stop loss order at $60/share

      D. stop buy order at $60/share

Suppose the market for toilet paper is perfectly competitive. The long run equilibrium is characterized by the price being $2 per roll with 20 firms making toilet paper, each selling 5 million rolls per week for a total of 100 million rolls being sold each week. A pandemic then breaks out, where people are afraid that the world will run out of toilet paper.

a) what happens in the short run to:

-1) The price of a roll of toilet paper?

-2) The number of firms making toilet paper?

-3) The amount of toilet paper made each week by each firm?

-4) weekly firms profits?

b) What happens in the long run in terms of (1-4) above, and what is the mechanism that brings about that change, assuming demand remains permanently elevated as people in the future are constantly worried that another pandemic will occur?

c) Graph the original long run equilibrium, the short run equilibrium, and the return to a long run equilibrium on two graphs, one for the market and one for the individual firm.

Suppose XER Inc. is a monopoly that produces a drug that cures the common cold. The weekly (inverse) market demand* for its product takes the form P=580-6Q, where Q is measured as the number of tablets. The marginal and average costs are $100 per tablet.

Solve for:

(a)  Solve for the weekly level of output (measured in the number of tablets per week) that will be produced by XER Inc. if it maximizes profits

(b) Solve for

(i) the profit-maximizing price-per tablet charged,

(ii) total weekly revenue and

(iii) the amount of economic profits earned by XER, Inc.

(c)

(i) Calculate the weekly quantity sold

(ii) Calculate the total weekly revenues for XER, Inc. IF the firm operated under perfectly competitive market conditions (i.e., assume that that XER faces the same demand curve but that, as in competitive markets, the equilibrium price and quantity is where P=MC.)

(d)

Compare answers to sub-questions a & b to those for sub-question c and assess the differences in output, prices, total revenues, total costs and economic/excess profits under the two different market conditions.

Suppose that the perfectly competitive market for coffee beans is made up of identical firms with long-run total cost functions given by T C = 2Q 3 − 24Q 2 + 80Q , where Q is 100,000 pounds of coffee beans. Assume that these cost functions are independent of the number of firms in the market and that firms may enter or exit the market freely. Market demand is Q = 100, 000 − 400P

(a) Find the long-run equilibrium price, the quantity produced by each firm, and the number of firms in the industry.

(b) Suppose that market demand increases to Q = 140, 000 − 400P , Solve for the new long-run competitive equilibrium and the number of firms in the industry under the new market demand condition.

You rent a room with a nice ocean view in a house on Del Playa. Last week’s storms severely eroded
the sea cliffs and your friend (the engineering major) estimates that there is a 50% chance that they
will collapse and you will lose all of your possessions, valued at $100. You can sell off some of your
belongings to buy some insurance against this risk, for the price of p dollars for every dollar of insurance.

Now suppose that your utility of wealth is given by u(c) = c. Write your new MRS. How much
insurance would you buy if p = .4? If p = .6?

Could you explane in detail,Please? And could you also graph it?

thank you!